On fixed points of central automorphisms of finite-by-nilpotent groups. (Q403045)
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scientific article; zbMATH DE number 6335786
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On fixed points of central automorphisms of finite-by-nilpotent groups. |
scientific article; zbMATH DE number 6335786 |
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On fixed points of central automorphisms of finite-by-nilpotent groups. (English)
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29 August 2014
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The authors prove that if \(G\) is a finite-by-nilpotent group whose central kernel \(K(G)\) (the subgroup of all elements fixed by every central automorphism) has finite index, then \(G\) is finite over the center and the elements of finite order form a finite group. If \(G\) is a finite-by-nilpotent group and \(G/K(G)\) is a Chernikov group, then \(G\) itself is a Chernikov group.
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central automorphisms
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central kernel
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finite-by-nilpotent groups
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Chernikov groups
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elements of finite order
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subgroups of finite index
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